SOLUTION: FIND THE EQUATION OF THE PARABOLA: Axis vertical and passing through (0,0) , (1,0) and (5,-20) the equation pls thank you so much:)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: FIND THE EQUATION OF THE PARABOLA: Axis vertical and passing through (0,0) , (1,0) and (5,-20) the equation pls thank you so much:)      Log On


   

Question 1187578: FIND THE EQUATION OF THE PARABOLA:
Axis vertical and passing through (0,0) , (1,0) and (5,-20)
the equation pls thank you so much:)
Found 3 solutions by MathLover1, ikleyn, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Axis vertical and passing through (0,0) , (1,0) and (5,-20)
the equation of the parabola is:
y=ax%5E2%2Bbx%2Bc
Since the parabola passes through the point (0,0), then 0=c
so we have
y=ax%5E2%2Bbx+
Since the parabola passes through the point (1,0), then
0=a%2A1%5E2%2Bb%2A1+
0=a%2Bb......solve for a
a=-b........eq.1
Since the parabola passes through the point (5,-20), then
-20=25a%2B5b ........substitute a from eq.1
-20=25%28-b%29%2B5b
-20=-25b%2B5b
-20=-20b
b=1
go to
a=-b........eq.1...substitute b
a=-1
your equation is:
y=-x%5E2%2Bx+





Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

            It can be done in much simpler way,


and I just answered this question/problem yesterday under the link


https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1187461.html

https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1187461.html


showing this simpler way.



It is interesting to me,  if you read,  at all,  the solutions, that the tutors develop for you and post to you ?


And if you read them,  then for what reason do you post the duplicate requests,  without explaining the meaning  WHY  you do that.




Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The function has zeros at 0 and 1, so the equation is of the form

y=a%28x-0%29%28x-1%29 or y=a%28x%29%28x-1%29

Use the coordinates of the other given point to determine the constant a:

-20=a%285%29%285-1%29
-20=20a
a=-1

The equation of the parabola is

y=-1%28x%29%28x-1%29
y=-1%28x%5E2-x%29
y=-x%5E2%2Bx